Falconer's \((K, d)\) distance set conjecture can fail for strictly convex sets \(K\) in \(\mathbb{R}^d\)

DOI10.4171/rmi/1254zbMath1470.28004OpenAlexW3127876859WikidataQ113691956 ScholiaQ113691956MaRDI QIDQ2039503

Hindy Drillick, Dimitrios Ntalampekos, Christopher J. Bishop

Publication date: 5 July 2021

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rmi/1254

zbMATH Keywords

convex setsHausdorff dimensiondistance setspolyhedral normsFalconer's conjecture

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Hausdorff and packing measures (28A78)

Related Items

On the Hausdorff dimension of the residual set of a packing by smooth curves ⋮ Every planar set has a conformally removable subset with the same Hausdorff dimension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Erdős distinct distances problem in the plane
• On Falconer's distance set conjecture
• Hausdorff dimension and distance sets
• On Falconer's distance set problem in the plane
• Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions
• Distance sets of well-distributed planar sets for polygonal norms
• Dimensions of intersections and distance sets for polyhedral norms
• On the Hausdorff dimensions of distance sets
• OPTIMAL SMOOTHING FOR CONVEX POLYTOPES
• What is Falconer's Conjecture?
• Convex Analysis
• Weighted restriction estimates and application to Falconer distance set problem